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Abstract:
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We use a fully Bayesian framework to semiparametrically estimate covariance functions of stationary Gaussian processes from irregularly-spaced data. The covariance functions are modeled in the spectral domain on the log-log scale using penalized natural splines, which results in a flexible class of smooth densities having power law tails. The Fourier transforms required to construct likelihoods from the spectral densities are computed using standard Monte Carlo integration. These calculations require massive computational effort, but are highly parallelizable. Using GPU technology, computational speeds are competitive with standard parametric covariance model estimation.
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